Two-dimensional px+ipy topological superconductors host gapless Majorana edge modes, as well as Majorana bound states at the core of h/2e vortices. Here we establish the possibility of realizing the fractional counterpart of this phase: a fractional chiral superconductor. This exotic phase is shown to give rise to a plethora of non-Abelian bulk excitations and a chiral Z2m parafermion theory on the edge of the sample, where m is an odd integer. In addition, we demonstrate that Z2m parafermionic bound states reside at the cores of h/2e vortices. In certain geometries, the system can support a fractional Josephson junction with 4πm periodicity, reflecting the underlying non-Abelian excitations. Finally, we show that the tunneling density of states associated with this edge theory exhibits an anomalous energy dependence of the form ωm−1. Our results are demonstrated through an explicit tractable model, composed of an array of coupled Rashba wires in the presence of strong interactions, Zeeman field, and proximity coupling to an s-wave superconductor.
